Statistical Methods for Biotechnology Products－Statistical Designs for Stability Studies

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Statistical Methods for

Biotechnology Products

Statistical Designs for Stability Studies

by

Jen-pei Liu, PhD, Professor

Division of Biometry, Department of Agronomy

National Taiwan University

and

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Outlines

 _{Statistical Concepts}

- Bias and variability - Confounding

- Interaction

 _{Basic Design Considerations}

- Design objective - Information needed - Design factors

- Response variables

- Regulatory requirements – ICH and FDA

 _{Stability Designs}

- Assumption - Design strategies

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Statistical Concepts



_Bias



_Variability



_Confounding



_Interaction

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Interaction and No Interaction

-1 1 X₁ -1 80 75 1 90 85         ) ( 1 ) ( 1 ) ( ) 20 ( 1 ) 10 ( 1 ) ( 2 1 blister bottle Package x mg mg Strength x Let No interaction x₂ Interaction x₂ -1 1 X₁ -1 80 85 1 90 75 10mg 20mg 10mg

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An Example

Condition Lot Package Strength Response Run X₁ X₂ X₃ X₄ Y 1 1 1 1 1 Y₁ 2 1 1 -1 -1 Y₂ 3 1 -1 1 -1 Y₃ 4 1 -1 -1 1 Y₄ 5 -1 1 1 -1 Y₅ 6 -1 1 -1 1 Y₆ 7 -1 -1 1 1 Y₇ 8 -1 -1 -1 -1 Y₈ -1 1 X₁ -1 Y_7,Y₈ Y_5,Y₆ 1 Y_3,Y₄ Y_1,Y₂ -1 1 X₃ -1 Y_2,Y₈ Y_4,Y₆ 1 Y_3,Y₅ Y_1,Y₇ X₂ X₄                    2 2 2 2 & 2 1 6 5 4 3 8 7 2 1 Y Y Y Y Y Y Y Y x x n Interactio

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Statistical Design



_{Design objectives}



_{Information needed}



_{Design factors}



_{Response variables}

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Design Objective



_{Minimize total sample size or minimize}

total cost in testing



_{Reduce number of assays at same time}

- Limited laboratory capacity

- Limited resources

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Information needed

 _{Marking requirements} - Package types - Specifications - Desired shelf-life

- When analyze_{？ ( submit to FDA)} - Where sold_？

 _{Manufacturing practices}

- Several strengths with same formula

- Common granulation batch into multiple strengths

- Common encapsulation batch into multiple package types

 _{Previous formulation study results}

- Factors that might affect stability - Storage conditions

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Information needed



_{Method variability}

- Between and within run CV’s



_{Sample variability}

- How to sample containers _？

- How to sample from containers _？



_{Manufacturing capacity}

- When will manufacture ？ - When will package ？

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Design Factors

 _Strength

 _{Package type}  _Batch

 _{Sampling (or storage) times}  _{Storage conditions}  _Replicates ？  _Analyst  _Location : etc.

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Response Variables



_{Potency (Quantitative)}



_{Dissolution (Quantitative)}



_{Appearance (Qualitative)}



_{Hardness (?)}



_{Color (?)}



_{Moisture (?)}

:

etc.

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Regulatory Requirements

ICH and FDA



_{Sampling Times}

“… Stability testing generally may be done at 3-month

intervals during the first year, 6-month intervals during the second year, and yearly thereafter…”

Sampling times: 0, 3, 6, 9, 12, 18, 24, 36, …



_{Number of batches required}

“… At least three primary batches and preferably more should be tested to allow for some estimate of batch-to-batch and to test the hypothesis that a single expiration

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Assumptions



_{The degradation curve is linear}

If there is an exponential decay, it may be

linearized by transformation: arithmetic or

logarthmic scale



_{Sampling times are fixed across all factors}

i.e.,

sampling time: 0, 3, 6, 9, 12, 18, 24, …

indirect assays

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Design Strategies



_{Complete factorial}

- Choose all combination of batch, strength, and package



_{Fractional factorial or matrixing}

- Any subset of a complete factorial design is considered a matrix design

- Choose fraction of batch, strength, and package combinations



_Bracketing

- Test only extremes e.g.,

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Design strategies

Sampling times T1= 0, 3, 6, 9, 12, 18, 24, 36, 48 T2= 0, 3, 9, 18, 36, 48 T3= 0, 6, 12, 24, 48 T5= 0, 3, 12, 36, 48 T6= 0, 6, 18, 48 T7= 0, 9, 24, 48 T8= 0, 3, 9, 12, 24, 36, 48 T9= 0, 3, 6, 12, 18, 36, 48 TA= 0, 6, 9, 18, 24, 48

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Stability Design

Type Factors Time Points

1 Complete All

2 Complete Partial

3 Matrixing All

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TABLE 10.3.5 NDA Stability Designs

Batch Strength Bottle Blister Tube Bottle Blister Tube Design 1: Complete factorial design Design 2: Complete-2/3 design 1 15 30 60 T₁ T₁ T₁ T₁ T₁ T₁ T₁ T₁ T₁ T₈ T₉ T_A T₉ T_A T₈ T_A T₈ T₉ 2 15 30 60 T₁ T₁ T₁ T₁ T₁ T₁ T₁ T₁ T₁ T_A T₈ T₉ T₈ T₉ T_A T₉ T_A T₈ 3 15 30 60 T₁ T₁ T T₁ T₁ T T₁ T₁ T T₉ T_A T T_A T₈ T T₈ T₉ T

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TABLE 10.3.5 Continued

Batch Strength Bottle Blister Tube Bottle Blister Tube Design 3: Complete -1/2 design Design 4: Complete-1/3 design 1 15 30 60 T₂ T₃ T₃ T₃ T₃ T₂ T₂ T₂ T₃ T₅ T₆ T₇ T₆ T₇ T₅ T₇ T₅ T₆ 2 15 30 60 T₂ T₂ T₃ T₂ T₃ T₃ T₃ T₃ T₂ T₇ T₅ T₆ T₅ T₆ T₇ T₆ T₇ T₅ 3 15 30 60 T₃ T₃ T T₂ T₂ T T₃ T₂ T T₆ T₇ T T₇ T₅ T T₅ T₆ T

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Batch Strength Bottle Blister Tube Bottle Blister Tube Design 5: Fractional

factorial design

Design 6: Two strength per batch design

1 15 30 60 T₁ T₁ — T₁ — T₁ — T₁ T₁ T₁ T₁ — T₁ T₁ — T₁ T₁ — 2 15 30 60 — T₁ T₁ T₁ T₁ — T₁ — T₁ — T₁ T₁ — T₁ T₁ — T₁ T₁ 3 15 30 60 T₁ — T — T₁ T T₁ T₁ — T₁ — T T₁ — T T₁ — T

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Batch Strength Bottle Blister Tube Bottle Blister Tube Design 7: Two packages

per strength design Design 8: Fractional-1/2 design

1 15 30 60 T₁ T₁ — — T₁ T₁ T₁ — T₁ T₂ T₃ — T₃ — T₂ — T₂ T₃ 2 15 30 60 T₁ T₁ — — T₁ T₁ T₁ — T₁ T₂ T₂ T₃ T₂ T₃ — T₃ — T₂ 3 15 30 60 T₁ T₁ — — T₁ T T₁ — T T₃ — T — T₂ T T₃ T₂ —

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Batch Strength Bottle Blister Tube Bottle Blister Tube Design 9: Two strength

per batch -1/2 design packages per strength Design 10: Two -1/2 design 1 15 30 60 T₁ T₁ — — T₁ T₁ T₁ — T₁ T₂ T₃ — T₃ — T₂ — T₂ T₃ 2 15 30 60 T₁ T₁ — — T₁ T₁ T₁ — T₁ T₂ T₂ T₃ T₂ T₃ — T₃ — T₂ 3 15 30 T₁ T₁ — T₁ T₁ — T₃ — — T₂ T₃ T₂

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TABLE 10.3.6 Number of Stability Tests Required for Various Designs

Type Design description Number of assays Percent reduced a — Complete 243 — I Complete -2/3 180 25.9 I Complete -1/2 142 41.6 I Complete -1/3 117 51.9 II Fractional 162 33.3

II Two strengths per batch 162 33.3

II Two packages per strength 162 33.3

III _{Fractional -1/2} 99 59.3

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Matrixing Designs



_Matrixing

_(ICH)

The design of a stability schedule such that a selected

subset of the total number of possible samples for all factor combinations is tested at a specified time point. At a

subsequent time point, another subset of samples for all factor combinations is tested.

Assumption: The stability of each subset of samples tested represented the stability of all samples at a given time

point.

The differences in the samples for the same drug

product should be identified as, for example, covering different

batches, different strengths, different sizes for the same container closure system, and , possibly in some cases,

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Matrixing design



_Example

Table 10.3.2 Two-Thirds Matrixing Design

Dosage strength/lot of granulation Package type 50 mg 75 mg 100 mg A B C A B C A B C Blister + + (+) (+) + + + (+) + HDPE1 (+) + + + (+) + + + (+) HDPE2 + (+) + + + (+) (+) + +

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Matrixing Designs



_{Example (ICH): Two Factors: One-half Reduction}

Time Points Strength Batch 0 3 6 9 12 18 24 36 1 1 T T - T T - T T 2 T T - T T T - T 3 T - T - T T - T 2 1 T - T - T - T T 2 T T - T T T - T 3 T - T - T - T T

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Matrixing Designs

 _{Example (ICH) Two Factors: One-third Reduction}

Time Points Strength Batch 0 3 6 9 12 18 24 36 1 1 T T - T T - T T 2 T T T - T T - T 3 T - T T T T T T 2 1 T - T T T T T T 2 T T - T T - T T 3 T T T - T T - T

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Matrixing Designs

 _{Example (ICH) Three Factors:}

Time Points 0 3 6 9 12 18 24 36 T1 T - T T T T T T T2 T T - T T - T T T3 T T T T - T T - T

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Matrixing Designs



_{Example (ICH) Three Factors:}

Design A Strength S1 S2 S3 Container Size A B C A B C A B C Batch 1 T1 T2 T3 T2 T3 T1 T3 T1 T2 Batch 2 T2 T3 T1 T3 T1 T2 T1 T2 T3 Batch 3 T3 T1 T2 T1 T2 T3 T2 T3 T1

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Matrixing Designs



_{Example (ICH) Three Factors:}

Design B Strength S1 S2 S3 Container Size A B C A B C A B C Batch 1 T1 T2 T2 T1 T1 T2 Batch 2 T3 T1 T3 T1 T1 T3 Batch 3 T3 T2 T2 T3 T2 T3

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Bracketing Designs



_{Bracketing (ICH)}

The design of a stability schedule such that only

samples on the extremes of certain design factors

(e.g., strength, package size( are tested at all time

points as in a full design.

Assumption: The stability of any immediate levels

is represented by the stability of the extremes

tested.

When a range of strengths is to be tested,

bracketing is applicable if the strengths are

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Bracketing design



_Example

TABLE 10.3.3 Example of Bracketing Design Storage condition Testing interval (month) Temp (oC) Relative humidity (%) 3 6 9 12 18 24 36 48 21 45 (+) (+) (+) (+) (+) (+) (+) (+) 25 60 + + + + + + + + 30 35 (+) (+) (+) (+) (+) (+) (+) (+) 30 70 + + + + + + + +

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Matrixing and bracketing design

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_Remarks

- A matrixing or bracketing design may be applicable to strength if there is no change in proportion of active ingredients,

container size, and intermediate sampling time points (Lin,1994) - A matrixing design is not recommended if there is a significant change in proportions of active ingredients

- A matrixing design should not be applied to sampling times at two endpoints (I.e., the initial and the lsat sampling time points) and at any time points beyond the desired expiration date

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